Bayesian Learning for Neural Networks: an algorithmic survey

The last decade witnessed a growing interest in Bayesian learning. Yet, the technicality of the topic and the multitude of ingredients involved therein, besides the complexity of turning theory into practical implementations, limit the use of the Bayesian learning paradigm, preventing its widespread adoption across different fields and applications. This self-contained survey engages and introduces readers to the principles and algorithms of Bayesian Learning for Neural Networks. It provides an introduction to the topic from an accessible, practical-algorithmic perspective. Upon providing a general introduction to Bayesian Neural Networks, we discuss and present both standard and recent approaches for Bayesian inference, with an emphasis on solutions relying on Variational Inference and the use of Natural gradients. We also discuss the use of manifold optimization as a state-of-the-art approach to Bayesian learning. We examine the characteristic properties of all the discussed methods, and provide pseudo-codes for their implementation, paying attention to practical aspects, such as the computation of the gradient

Inference in Bayesian Networks

Tato diplomová práce se zabývá demonstrací různých přístupů k inferencím v Bayesovských sítích. V teoretické části jsou rozebrány základy pravděpodobnosti, základy teorie Bayesovkých sítí, inferenční metody a oblasti aplikací Bayesovských sítí. Inferenční metody jsou krátce představeny a doplněny jejich algoritmem. Princip každé metody je uveden na příkladu. Praktická část obsahuje popis implementace, experimenty s demonstračními aplikacemi a shrnutí dosažených výsledků.This master's thesis deals with demonstration of various approaches to probabilistic inference in Bayesian networks. Basics of probability theory, introduction to Bayesian networks, methods for Bayesian inference and applications of Bayesian networks are described in theoretical part. Inference techniques are explained and complemented by their algorithm. Techniques are also illustrated on example. Practical part contains implementation description, experiments with demonstration applications and conclusion of the results.

A Primer on Bayesian Neural Networks: Review and Debates

Neural networks have achieved remarkable performance across various problem domains, but their widespread applicability is hindered by inherent limitations such as overconfidence in predictions, lack of interpretability, and vulnerability to adversarial attacks. To address these challenges, Bayesian neural networks (BNNs) have emerged as a compelling extension of conventional neural networks, integrating uncertainty estimation into their predictive capabilities. This comprehensive primer presents a systematic introduction to the fundamental concepts of neural networks and Bayesian inference, elucidating their synergistic integration for the development of BNNs. The target audience comprises statisticians with a potential background in Bayesian methods but lacking deep learning expertise, as well as machine learners proficient in deep neural networks but with limited exposure to Bayesian statistics. We provide an overview of commonly employed priors, examining their impact on model behavior and performance. Additionally, we delve into the practical considerations associated with training and inference in BNNs. Furthermore, we explore advanced topics within the realm of BNN research, acknowledging the existence of ongoing debates and controversies. By offering insights into cutting-edge developments, this primer not only equips researchers and practitioners with a solid foundation in BNNs, but also illuminates the potential applications of this dynamic field. As a valuable resource, it fosters an understanding of BNNs and their promising prospects, facilitating further advancements in the pursuit of knowledge and innovation.Comment: 65 page

Dropout Inference in Bayesian Neural Networks with Alpha-divergences

To obtain uncertainty estimates with real-world Bayesian deep learning models, practical inference approximations are needed. Dropout variational inference (VI) for example has been used for machine vision and medical applications, but VI can severely underestimates model uncertainty. Alpha-divergences are alternative divergences to VI's KL objective, which are able to avoid VI's uncertainty underestimation. But these are hard to use in practice: existing techniques can only use Gaussian approximating distributions, and require existing models to be changed radically, thus are of limited use for practitioners. We propose a re-parametrisation of the alpha-divergence objectives, deriving a simple inference technique which, together with dropout, can be easily implemented with existing models by simply changing the loss of the model. We demonstrate improved uncertainty estimates and accuracy compared to VI in dropout networks. We study our model's epistemic uncertainty far away from the data using adversarial images, showing that these can be distinguished from non-adversarial images by examining our model's uncertainty

Intrusion Detection System using Bayesian Network Modeling

Computer Network Security has become a critical and important issue due to ever increasing cyber-crimes. Cybercrimes are spanning from simple piracy crimes to information theft in international terrorism. Defence security agencies and other militarily related organizations are highly concerned about the confidentiality and access control of the stored data. Therefore, it is really important to investigate on Intrusion Detection System (IDS) to detect and prevent cybercrimes to protect these systems. This research proposes a novel distributed IDS to detect and prevent attacks such as denial service, probes, user to root and remote to user attacks. In this work, we propose an IDS based on Bayesian network classification modelling technique. Bayesian networks are popular for adaptive learning, modelling diversity network traffic data for meaningful classification details. The proposed model has an anomaly based IDS with an adaptive learning process. Therefore, Bayesian networks have been applied to build a robust and accurate IDS. The proposed IDS has been evaluated against the KDD DAPRA dataset which was designed for network IDS evaluation. The research methodology consists of four different Bayesian networks as classification models, where each of these classifier models are interconnected and communicated to predict on incoming network traffic data. Each designed Bayesian network model is capable of detecting a major category of attack such as denial of service (DoS). However, all four Bayesian networks work together to pass the information of the classification model to calibrate the IDS system. The proposed IDS shows the ability of detecting novel attacks by continuing learning with different datasets. The testing dataset constructed by sampling the original KDD dataset to contain balance number of attacks and normal connections. The experiments show that the proposed system is effective in detecting attacks in the test dataset and is highly accurate in detecting all major attacks recorded in DARPA dataset. The proposed IDS consists with a promising approach for anomaly based intrusion detection in distributed systems. Furthermore, the practical implementation of the proposed IDS system can be utilized to train and detect attacks in live network traffi